ERC Starting grant – Waves propagation in real life physics occur in media which are neither homogeneous or spatially infinity. The birth of radar/sonar technologies (and the raise of computed tomography) greatly motivated numerous developments in microlocal analysis and the linear theory. Only recently toy nonlinear models have been studied on a curved background, sometimes compact or rough. Understanding how to extend such tools, dealing with wave dispersion or focusing, will allow us to significantly progress in our mathematical understanding of physically relevant models. There, boundaries appear naturally and most earlier developments related to propagation of singularities in this context have limited scope with respect to crucial dispersive effects. Despite great progress over the last decade, driven by the study of quasilinear equations, our knowledge is still very limited. Going beyond this recent activity requires new tools whose development is at the heart of this proposal, including good approximate solutions going over arbitrarily large numbers of caustics, sharp pointwise bounds on Green functions, development of efficient wave packets methods, quantitative refinements of propagation of singularities (with direct applications in control theory), only to name a few important ones.

Oana Ivanovici

PI of the ERC Starting grant ANADEL

CNRS Senior Researcher at LJLL

part-time Professor at Ecole Polytechnique

_{oana.ivanovici "AT" math.cnrs.fr}

Research interests : microlocal analysis, nonlinear PDE, hyperbolic equations on manifolds with or without boundary, dispersion, long time behaviour of solutions, propagation and reflection of singularities, diffraction phenomenon.

Editorial work : I am an associated editor for :

“Bulletin des Sciences Mathématiques“.

“Advances in Continuous and Discrete Models: Theory and Applications”.

Volunteer experience : since May 2022 I am an elected member of the CLAS de Jussieu Comité d’action Sociale du CNRS (CAES).

You can find some of my paintings and drawings here.